ATTEMPT TO SOLVE A COMBINATORIAL PROBLEM IN THE CONTINUUM BY A METHOD OF EXTENSION-REDUCTION.

Combinatorial optimization problems in n variables are formulated as nonlinear programming problems in (n-1)**2 variables and n**2 constraints. Methods for solving the large unconstrained optimization problem generated are considered, with emphasis on conjugate-gradient algorithms based on the homogeneous model. The quadratic assignment problem is considered as an example and results from the nonlinear programming approach are discussed.